Density Calculator
Solve ρ = m ÷ V for density, mass or volume, with the rearranged formula shown for whichever direction you pick.
ρ = m ÷ V
Density (kg/m³)
Formula used for this direction
ρ = m ÷ V
Your values
m = 1 kg, V = 0.001
Volume cannot be zero.
Mass Packed Into Space
Density answers a simple question: how much matter is packed into a given amount of space? It is mass divided by volume, ρ = m ÷ V, and it is the property that decides what floats, what sinks, and how heavy an object of a given size turns out to be.
All three quantities are solvable. V = m ÷ ρ finds the space a known mass occupies, and m = ρ·V finds the mass of a known volume — the direction you want when estimating the weight of something you can measure but not lift.
Worked example — water as the reference
One kilogram of water occupies one litre, which is 0.001 m³:
ρ = 1 ÷ 0.001 = 1,000 kg/m³
That figure is not a coincidence — the litre and the kilogram were originally defined so that a litre of water would weigh a kilogram, and a litre of water still masses 1 kg today.
A second example, solving the other way. A 5 kg block of a material at 2,500 kg/m³ occupies V = 5 ÷ 2500 = 0.002 m³, which is 2 litres. Turn it around: 0.002 m³ of that same material masses 5 kg.
And a small sample: 500 g in 250 cm³ gives 2,000 kg/m³ — twice the density of water, so it sinks.
Common mistake
Mixing cubic centimetres with kilograms. A density in g/cm³ and one in kg/m³ differ by a factor of exactly 1000, and dropping that factor produces answers wrong by three orders of magnitude. Decide which system you are in before you start, and keep volumes in cubic metres if your masses are in kilograms.
Volume Occupied by the Same Mass
The identical mass takes up very different space depending on the material. Computed with V = m ÷ ρ, comparing water at 1,000 kg/m³ against steel at 7,850 kg/m³.
| Mass | As water | As steel |
|---|---|---|
| 0.5 kg | 0.5 litres | 0.06369 litres |
| 1 kg | 1 litres | 0.1274 litres |
| 2 kg | 2 litres | 0.2548 litres |
| 5 kg | 5 litres | 0.6369 litres |
| 10 kg | 10 litres | 1.274 litres |
The two density figures used in this table are the widely quoted nominal values for pure water and typical carbon steel, included to illustrate the arithmetic rather than as precise material specifications — real steel varies with alloy and real water varies with temperature. Enter your own measured density above for an exact answer.
Keep going
- A fluid's density sets how fast pressure builds with depth, since hydrostatic pressure is ρgh; the pressure calculator includes that depth calculation. Pressure Calculator
- Density gives you mass from a volume, and mass is what Newton's second law needs; the force calculator takes that mass and an acceleration. Force Calculator
Frequently Asked Questions
What is the density formula?
ρ = m ÷ V — mass divided by volume. In SI units that gives kilograms per cubic metre. The common alternative, grams per cubic centimetre, is exactly 1000 times larger: water is 1000 kg/m³ or 1.00 g/cm³, the same physical thing written two ways.
Why does ice float on water?
Because ice is less dense than liquid water — water is unusual in expanding as it freezes, so the same mass occupies more volume. Anything less dense than the fluid around it floats, which is why the solid form of almost every other substance sinks in its own liquid.
How do I find volume from density and mass?
Rearrange to V = m ÷ ρ. A 5 kg block of a material with density 2500 kg/m³ occupies 5 ÷ 2500 = 0.002 m³, which is 2 litres. This calculator solves that direction directly.
What is the difference between density and specific gravity?
Specific gravity is a ratio: a material's density divided by water's, making it dimensionless. A specific gravity of 2.5 means two and a half times as dense as water. It is convenient precisely because it carries no units and so reads the same in every measurement system.
Does density change with temperature?
Yes, for essentially every material. Heating usually expands a substance, increasing volume while mass stays fixed, so density falls. The effect is small for solids and liquids over ordinary ranges but very large for gases, which is why hot air rises and why gas densities are always quoted with a temperature and pressure attached.
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